Imagine there's a strong laser beam, not just an attenuated stream of single photons, entering a balanced Mach-Zehnder interferometer.
One-photon picture: Each photon interferes with itself on the second beam splitter. As a result, all photons leave out of the same output.
More realistic picture: If the intensity of the laser is strong enough, a lot of photons will enter the interferometer within the coherence time and will be therefore indistinguishable (at least by their arrival time).
How does this fact change the quantum mechanical description of the state? Shouldn’t there be a two-photon interference at the second beam splitter in this case? How do you describe the evolution of the state throughout the interferometer mathematically: two-photon interference of photons that are themselves in the same superposition of two paths?